Question

Rauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers (located in cities A, B, and C). As shown in the table below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following information: Location Coordinates (miles) Deliveries per day A (100,300) 4 B (400,100) 3 C (300,200) 9 a. Which of these three locations yields the smallest load-distance score, based on Euclidean distances? Location _(A,B,C)_ yields the smallest load-distance score of _(Enter your response rounded to one decimal place.)_ b. Which of these locations is best, based on rectilinear distances? Location _(A,B,C)_ is the best, yielding a load-distance score of _(Enter your response as a whole number.)_ c. What are the coordinates of the center of gravity? The center of gravity is x* = _(Enter your response rounded to one decimal place.)_ miles, y* = _(Enter your response rounded to one decimal place.)_ miles.

          Rauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers (located in cities A, B, and C). As shown in the table below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following information:

Location Coordinates (miles) Deliveries per day
A (100,300) 4
B (400,100) 3
C (300,200) 9

a. Which of these three locations yields the smallest load-distance score, based on Euclidean distances?
Location _(A,B,C)_ yields the smallest load-distance score of _(Enter your response rounded to one decimal place.)_

b. Which of these locations is best, based on rectilinear distances?
Location _(A,B,C)_ is the best, yielding a load-distance score of _(Enter your response as a whole number.)_

c. What are the coordinates of the center of gravity?
The center of gravity is x* = _(Enter your response rounded to one decimal place.)_ miles, y* = _(Enter your response rounded to one decimal place.)_ miles.

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Added by Benjamin C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Madhur L

01/20/2023

Step 1

The Euclidean distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Show more…

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Rauschenberg Manufacturing is investigating which locations would best position its new plant relative to three important customers (located in cities A, B, and C). As shown in the table below, all three customers require multiple daily deliveries. Management limited the search for this plant to those three locations and compiled the following information: Location Coordinates (miles) Deliveries per day A (100,300) 4 B (400,100) 3 C (300,200) 9 a. Which of these three locations yields the smallest load-distance score, based on Euclidean distances? Location _(A,B,C)_ yields the smallest load-distance score of _(Enter your response rounded to one decimal place.)_ b. Which of these locations is best, based on rectilinear distances? Location _(A,B,C)_ is the best, yielding a load-distance score of _(Enter your response as a whole number.)_ c. What are the coordinates of the center of gravity? The center of gravity is x* = _(Enter your response rounded to one decimal place.)_ miles, y* = _(Enter your response rounded to one decimal place.)_ miles.

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Transcript

00:01 Hello students, according to the given question we have to calculate euclidean distances between each location with the help of the following formula.

00:13 So the formula is tab is equal to xa minus xb whole square plus y a minus y b minus y b whole square plus y a minus y b whole square.

00:32 Whole power 1 by 2.

00:36 By substituting we get 100 minus 400 whole square plus 200 minus 100 whole square whole power 1 by 2 which is equal to 90 ,000 plus 10 ,000 whole power 1 by 2.

01:06 Which is equal to 316 .23.

01:12 Now the distance for vc, that is d, d, dc is equal to xc minus xc whole square plus yb minus yc whole power 1 by 2.

01:35 By substituting we get 400 minus 100 whole square plus 100 minus 100 whole power 1 by 2.

01:53 We get 300.

01:57 For the distance, ca is equal to the formula xc minus xa whole square whole square whole power 1 by 2.

02:08 Plus yc minus ya whole square whole power 1 by 2.

02:15 By substituting we get 100 minus 100 whole square plus 100 minus 200 whole square whole power 1 by 2 which is equal to 100 so the euclidean distances are ab is equal to 316 .23 and bc is equal to 300 and for ca is equal to 100.

02:53 Here the total travel distance is equal to euclidean distance.

03:11 So deliveries per day of the destination point from a to b, is equal to 316 .23 into 4 which is equal to 1264 .92.

03:32 So the table will look like this.

03:35 So by observing all the totals, that is for the a total b and c, the location a yields the smallest total travel distance, that is in option a location a yields the smallest total travel that is 1564 .92 miles...

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